2.2 Heart transplants, Part II. Exercise 1.50 introduces the Stanford Heart Transplant Study. Of the 34 patients in the control group, 4 were alive at the end of the study. Of the 69 patients in the treatment group, 24 were alive. The contingency table below summarizes these results. Outcome Alive Dead Total Group Control Treatment 4 24 30 45 34 69 Total 28 75 103 (a) What proportion of patients in the treatment group and what proportion of patients in the control group died? (b) One approach for investigating whether or not the treatment is effective is to use a random- ization technique. i. What are the claims being tested? Use the same null and alternative hypothesis notation used in the section. ii. The paragraph below describes the set up for such approach, if we were to do it with- out using statistical software. Fill in the blanks with a number or phrase, whichever is appropriate We write alive on cards representing patients who were alive at the end of the study, and dead on cards representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size representing treatment, and another group of size representing control. We calculate the difference between the proportion of dead cards in the treatment and control groups (treatment - control) and record this value. We repeat this many times to build a distribution centered at Lastly, we calculate the fraction of simulations where the simulated differences in proportions are If this fraction is low, we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative. iii. What do the simulation results shown below suggest about the effectiveness of the trans- plant program? 2.2 Heart transplants, Part II. Exercise 1.50 introduces the Stanford Heart Transplant Study. Of the 34 patients in the control group, 4 were alive at the end of the study. Of the 69 patients in the treatment group, 24 were alive. The contingency table below summarizes these results. Outcome Alive Dead Total Group Control Treatment 4 24 30 45 34 69 Total 28 75 103 (a) What proportion of patients in the treatment group and what proportion of patients in the control group died? (b) One approach for investigating whether or not the treatment is effective is to use a random- ization technique. i. What are the claims being tested? Use the same null and alternative hypothesis notation used in the section. ii. The paragraph below describes the set up for such approach, if we were to do it with- out using statistical software. Fill in the blanks with a number or phrase, whichever is appropriate We write alive on cards representing patients who were alive at the end of the study, and dead on cards representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size representing treatment, and another group of size representing control. We calculate the difference between the proportion of dead cards in the treatment and control groups (treatment - control) and record this value. We repeat this many times to build a distribution centered at Lastly, we calculate the fraction of simulations where the simulated differences in proportions are If this fraction is low, we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative. iii. What do the simulation results shown below suggest about the effectiveness of the trans- plant program